I use the "Cloud" every day.
Using dropbox I have a centralized folder on all of my PC's.
Change a file on one and it automaticly changes it the others.
I have all of my pc's and the company pc's set up with dropbox and Logmein.
Logmein lets me access any of my pc's from any pc with internet access.
So the real basis of "Cloud Computing" is access to any of your files and pc
from anywhere. You can have a personal cloud that lets you do this or
freebies like Dropbox and Logmein that provide this service.
If you have Windows 7 (or Vista ARGH!!) you can use Microsoft's
Live Essentials to create your own cloud.
I'm certainly no expert, but here's what I think I've picked up about it.
We used to have our data on a computer, worked on it with programs on that computer, and if we wanted the data somewhere else we took steps to move it over the available data paths to that specific other place.
Now the trend is to keep your data, even to the point of your computer desktop configuration, and the library of programs to work on the data, on some computer out there somewhere, provided as a service, and let that service provider worry about doing the more intensive computations, backing up the data, and making it available wherever it is needed. You don't really know where the data and the computation are and it might not be all in one place. It's just somewhere in the cloud. It is sometimes compared to the electric power grid - you don't generate your electricity and don't care where it is generated. You are just hooked to the grid and consume it on demand.
The advantage is that you can access it from any and all computers with the right password, can have huge amounts of data for everybody to access, and you don't have to decide to where to send it. A downside is that you really have to trust the security of whoever is providing this service. And you have to plan ahead to be able to use your data somewhere that you won't be connected to the "cloud".